Fast and scalable Gaussian process modeling with applications to astronomical time series

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.Comment: Updated in response to referee. Submitted to the AAS Journals. Comments (still) welcome. Code available: https://github.com/dfm/celerit

Inferring probabilistic stellar rotation periods using Gaussian processes

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalising over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these 1132 Kepler objects of interest and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterising star-planet interactions. The code used to implement this method is available online.Comment: Submitted to MNRAS. Replaced 27/06/2017: corrections made to koi_periods.cs

Loose Ends for the Exomoon Candidate Host Kepler-1625b

The claim of an exomoon candidate in the Kepler-1625b system has generated substantial discussion regarding possible alternative explanations for the purported signal. In this work we examine in detail these possibilities. First, the effect of more flexible trend models is explored and we show that sufficiently flexible models are capable of attenuating the signal, although this is an expected byproduct of invoking such models. We also explore trend models using X and Y centroid positions and show that there is no data-driven impetus to adopt such models over temporal ones. We quantify the probability that the 500 ppm moon-like dip could be caused by a Neptune-sized transiting planet to be < 0.75%. We show that neither autocorrelation, Gaussian processes nor a Lomb-Scargle periodogram are able to recover a stellar rotation period, demonstrating that K1625 is a quiet star with periodic behavior < 200 ppm. Through injection and recovery tests, we find that the star does not exhibit a tendency to introduce false-positive dip-like features above that of pure Gaussian noise. Finally, we address a recent re-analysis by Kreidberg et al (2019) and show that the difference in conclusions is not from differing systematics models but rather the reduction itself. We show that their reduction exhibits i) slightly higher intra-orbit and post-fit residual scatter, ii) $\simeq$ 900 ppm larger flux offset at the visit change, iii) $\simeq$ 2 times larger Y-centroid variations, and iv) $\simeq$ 3.5 times stronger flux-centroid correlation coefficient than the original analysis. These points could be explained by larger systematics in their reduction, potentially impacting their conclusions.Comment: 21 pages, 4 tables, 11 figures. Accepted for publication in The Astronomical Journal, January 202

In vivo and in vitro studies on docosahexaenoic acid in traumatic brain injury

PhDTraumatic brain injury (TBI) is a devastating disease causing disability and death, and currently there are no effective treatments available. Therefore, there is an utmost need to improve our understanding of the pathophysiology of TBI and to identify potential therapies that can provide neuroprotection after injury. The aims of this thesis were to develop an in vivo and in vitro model of TBI, in which to assess the potential neuroprotective effects of an omega-3 polyunsaturated fatty acid (PUFAs), docosahexaenoic acid (DHA). Method The controlled cortical impact (CCI) in vivo model of TBI was optimized and performed in mice. Both a behavioural (Morris water maze (MWM) for cognitive deficits) and histological endpoints (astrogliosis, lesion size and activated microglia) were used to assess severity and neuroprotective effects of DHA. An in vitro model of mechanical TBI was also set up and optimized. This model employed 3D astrocyte cultures obtained from GFP positive rat pups. The CCI impactor from the in vivo studies was used to damage the cultures, and at 24 hours, 5 days and 10 days the astrogliosis and cell number was measured. Results The optimization of the in vivo studies demonstrated that at impaction depth of 2.2 mm produced an injury that was significantly different to the sham injury, in MWM performance and increased astrogliosis. Interestingly, there was an increase in the amount of astrogliosis on the contralateral side of the brain. A second study performed using the 2.2 mm injury parameters was performed, where an injection of DHA was administered via the tail vein 30 min after injury. The DHA-treated group did not demonstrate any neuroprotection compared to the injury-only group. However, there was an increase in the amount of astrogliosis in the contralateral hippocampus of the DHA-treat group. In the fat-1 studies it was shown that older male mice performed worse in the MWM, that the fat-1 gene did not confer neuroprotection but did lead to increased astrogliosis. The in vitro study revealed that astrocytes in the lesioned gels demonstrated an increase in astrogliosis, there was also an increase in the number of cell in the cultures following the lesion. Conclusion In conclusion, the in vivo model of CCI replicated components of the human TBI including a behavioural deficit and pathophysiological changes. Omega-3 PUFAs failed to demonstrate functional neuroprotection in this model, but histologically, promoted an increase in reactive astrogliosis. The development of a novel in vitro model of focal injury in a 3D culture system, that elicits reactive astrogliosis, could be used to support further studies of the astrocytic responses to mechanical injury.Medical Research Counci

Phenotypic switching of antibiotic resistance circumvents permanent costs in Staphylococcus aureus

AbstractBacterial antibiotic resistance is often associated with a fitness cost in the absence of the antibiotic [1, 2]. We have examined a resistance mechanism in Staphylococcus aureus that negates these costs. Exposure to gentamicin both in vitro and in vivo has been reported to result in the emergence of a gentamicin-resistant small colony variant (SCV) [3–8]. We show that the emergence of SCVs following exposure to gentamicin results from a rapid switch and that bacteria exposed to cycles of gentamicin followed by antibiotic-free medium repeatedly switched between a resistant SCV and a sensitive parental phenotype (revertants). The fitness of revertants relative to S. aureus with stable gentamicin resistance was greater in drug-free media, which suggests that S. aureus has evolved an inducible and reversible resistance mechanism that circumvents a permanent cost to fitness